car only starts atfer it sits for 10 min

[Brandonman38]

mother in law has a 95 lumina 3.1
went for a ride with her the other day and the car would not start she was ok with this and said wait ten min and it would start right up me being me started looking for what could be wrong tried to start the car over and over looking at this and that found nothing
ok car has to sit about 10 min from the last time you try to start it
it cranks fine and sounds like it starts to turn over for a sec but then nothing
tried messing with the gas but nothing fuel pump primes when you turn the key so its working is there a sensor or something that might cause this?
also the engine light comes on after you drive the car for a bit but is not on when the car has just started
if anyone could help me get in good with the mother in law (as good as you can ) i would appreciate it

[LMP]

This description repeats dozen times in all GM forums with the 3.1 and the usual culprit and solution is the ignition module/position sensor, part of the distributor. So have these components - not expensive and easy to replace - checked as a first step and in all probability, the search will be over.